Holomorphic Factorization at the Quantum Horizon

Abstract: We identify a horizon-skimming limit under which wave equations around large classes of black holes allow a determination of their low-lying (quasi-)degenerate normal modes. Building on our recent work, we use these quantum horizon" normal modes to study the thermodynamics of the parent black holes. A key observation is that the UV inputs (the location of the UV regulator, the number of species, and the cut-off in the angular Casimir quantum number) can all be combined into the freedom in a single real parameter. Remarkably, this parameter has an interpretation as the central charge of a holomorphically factorized 2D CFT, and choosing it to be the Kerr-CFT value reproduces the black hole's detailed thermodynamics from the statistical mechanics of normal modes. This perspective provides a heuristic understanding for why the Kerr-CFT central charge is related to the angular momentum of the black hole. The black holes we consider include Kerr-Newman in 3+1 dimensions and Cvetic-Youm in 4+1 dimensions (with all six charges), and they need not be BPS or extremal. Our results show that a refined version of the 't Hooftian quantum gas can be made fully consistent with the thermodynamics of very general black holes. Thismechanical" approach to the central charge is not directly reliant on asymptotic symmetries in the extremal limit, where the black hole is often unstable.